By Sara Finegan

         An inordinate number of kids are growing up without learning their multiplication facts.  Some of this is due to the prevalent use of calculators.  Some is due to the fact that there’s been an overall rejection of rote learning – throwing the baby out with the bathwater, in this case, I think.  Some of it is due to low numeracy as a result of math disabilities. 

         Many kids with learning disabilities really struggle with numbers and their values.  And, I think, it also has to do with processing memory and retention of information that isn’t used on a regular basis.

         I think there’s a place for rote learning of math facts in a demanding classroom.   The only way to learn multiplication facts and what happens when you add ten to a number is to recite them over and over in some way or another. 

         The way I use is skip-counting.  Skip-counting can be done starting at any age, and should continue to be done if not daily, then at least several times a week once the kids know the routine.

 I cannot stress enough the importance of visual cuing when it comes to math.  In this case, a giant number line, or individual number lines to 100 for each student are  in order.  You can also use individual multiplication charts or a giant one; the point is that the kids have to have the numbers 1-100 in front of them when they are skip-counting, at least during the first few months.

           A lot of teachers practice skip-counting with their students through 3, 4, and 5 multiplication facts, and then stop.  As a result, many kids know their multiplication facts through five, and can’t go higher.  Don’t let this happen.

         It can be a part of your daily routine to start with 3, and have the kids skip-count to 60.  Move to 4, then 5, and 6.  Once they know those, move to 7 and 8.  Practice them religiously.  I like to point at the numbers on a chart or number line with a pointer or a yardstick at first, but later it becomes a favorite reward for a student to be allowed to stand at the front of the class and cue the numbers. 

         It doesn’t take long for kids to internalize the facts as they continue to skip-count regularly.  But here’s the deal:  You can’t stop here. 

         One mistake I’ve seen over and over again is special educators working on skip-counting with their students and then never extending the skill into actual math problems.  And when I say “actual math problems,” I don’t mean a standard multiplication worksheet.  I mean math problems that require critical thinking.

         There’s no point in rote learning unless the information learned by rote is applied in complex situations.  Skip-counting alone, in a vacuum, has little meaning.  We need our students to be able to use the math facts to solve word problems, to reason through division problems, to figure out the value of x, and to  calculate prices and amounts. 

          So teach the multiplication facts by rote, but then require your students to use them, and use them in a variety of ways.  Only in this way will they truly be learning.

          In a demanding classroom, rote memorization has a place in supporting mastery of facts to be used in deeper-level situations.

critical thinking · demanding classroom · high expectations · learning disabilities · learning disabled · low numeracy · mastery · math fluency · math language · multiplication · Nimble with Numbers · processing · rigor · rigorous instruction · rote learning · skip counting · special education · standards · visual cuing

 By Sara Finegan 

         Last year I started a program I called “Nimble with Numbers.”  Before each math lesson, and sometimes before we started reading and writing instruction, we’d do math problems.  But we never used paper.  We used language and our heads, and worked through them out loud. 

         It became one of my students’ favorite activities, and we continue it to this day.

          Nimble with Numbers involves what I think of as math fluency – the ability to work with numbers in creative ways to get to an answer.  Here’s an example of what we do:.

         Using the document camera, I will write a couple of numbers – with no operation expressions.  And I will ask out loud for an answer.  This is what it looks like:

 Me:   (writing the numbers 36 and 72).  What’s the difference between 36 and 72?

Students:  Oh!  Oh!  Let me!

Me:  Ok……..Brandon.  Give it a whack.

Brandon:  Well, 36 to 46 is ten.  And 46 to 56 is another ten.  56 to 66 is ten.

 Me:  Ok, so how many do we have so far.

 Brandon:   Thirty.  Ten and ten and ten.

Me:    Ok.

 Brandon:    And 66 to 70 is …67, 68. 69….four.

Me:     Four.  Ok.  So what do we have now?

 Brandon:  Thirty-four. 

Me:    Ok.

Brandon:    And 70 to 72 is two more.  So thirty six. 

Me:    So what is the answer?

 Brandon:   The difference between 36 and 72 is thirty six.

         We do this with multiplication, addition, and subtraction, always using the proper vocabulary (difference, sum, product). 

          What I have discovered is that TALKING our way through math problems embeds the skills and opens up the synapses for math reasoning in a way that nothing else has in my classroom.    The ability to explain our reasoning is an added benefit:  the real gift for my kids has been the development of fluency in their approach to math problem-solving by moving to friendly numbers and taking things step by step.

Another example:

Me:    Ok.  How many legs do 456 elephants have?  (Writing 456.)

 Kids:   Me!  Oh me!  Me! Me! Me!

 Me:     Hmmm.  Mariana.

 Mariana:   Well, 456 is really four hundred plus fifty plus six.

Me:   Uhuh. 

 Mariana:   And an elephant has four legs.

 Me:    Yep.

 Mariana:   Four legs times 400 elephants is……….four times four is 16.  So since it’s four times 400, we’re going to add two zeros to that number in the ones and tens places.  So that’s 1600.

 Me:     Uhuh.

 Mariana:   Then, four times 50 is……well, four times five is 20.  But 50 is five tens, not five ones.  So it’s 200.  

Me:     Uhuh.  What do we have so far? 

 Mariana:  Sixteen hundred and two hundred is eighteen hundred.

 Me:    Ok.

 Mariana:  So four times six elephants is 24 elephants.  So four hundred and twenty six elephants have eighteen hundred and twenty-four legs.

 Me:     Applause. 

         In a demanding classroom, the kids do the work.  The teacher calls on people and facilitates.

demanding classroom · high expectations · learning disabled · math fluency · math language · Nimble with Numbers · rigor · rigorous instruction · special education · standards